As the signings of Negredo and Jovetic were completed on Friday, Pellegrini was back in Chile after leaving South Africa to attend to personal business.
It appears the deposed English champions have much to do to be ready to host Newcastle in a month in their season-opener after losing both games in South Africa against teams that finished only sixth and 12th in the local league. City scored one goal in 180 minutes of football, through midfielder James Milner.
City players have talked about a "drip-feed" system in early trainings in South Africa, where Pellegrini's unfamiliar tactics, which were formed in Chile and mainly in Spain, are being passed on gradually.
"It's logical at the beginning there is a lot of detail, so the players are looking, saying 'what is this one?'" Pellegrini said on City's website. "But they work very, very hard with us. (I'm) not trying to give all my ideas in just one or two weeks."
Having started at City with a 2-0 loss to Supersport United, Pellegrini unexpectedly flew out of South Africa early Thursday to fly to Chile and wasn't present to watch his team go down 2-1 to AmaZulu.
It's unclear how long Pellegrini will be away.
"Everybody missed the boss, his presence here," assistant manager Brian Kidd said following the loss to AmaZulu in Durban. "The work the boss has been doing is first class."
Goalkeeper Joe Hart said City hadn't made as much progress as hoped in South Africa, where the squad will remain for a little longer, soaking up the mild winter sunshine on the east coast before a two-game tour of Hong Kong next week.
"We're getting to know the new staff and things. It'll all click soon," Hart said. "We'd like it to be soon. Obviously we're very disappointed with the tour results. Things will come good."